小波去噪.zip_小波变换_小波去噪声_matlab例程_数值算法/人工智能下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/639f8b128449b3069de7262d/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/639f8b128449b3069de7262d/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">小波去噪</div><div class="t m0 x1 h4 y3 ff1 fs1 fc1 sc0 ls0 ws0">从信号学的角度看 <span class="ff2">,</span>小波去噪是一个信号滤波的问题。尽管在很大程度上小波去噪可以看成是低通滤波 <span class="ff2">,</span>但由于在去噪</div><div class="t m0 x1 h4 y4 ff1 fs1 fc1 sc0 ls0 ws0">后 <span class="ff2">,</span>还能成功地保留信号特征 <span class="ff2">,</span>所以在这一点上又优于传统的低通滤波器。由此可见 <span class="ff2">,</span>小波去噪实际上是特征提取和低通</div><div class="t m0 x1 h4 y5 ff1 fs1 fc1 sc0 ls0 ws0">滤波的综合 <span class="ff2">,</span>其流程图如下所示：</div><div class="t m0 x1 h5 y6 ff2 fs2 fc1 sc0 ls0 ws0">  </div><div class="t m0 x1 h4 y7 ff1 fs1 fc1 sc0 ls0 ws0">一个含噪的模型可以表示如下：</div><div class="t m0 x1 h6 y8 ff2 fs1 fc1 sc0 ls0 ws0">  </div><div class="t m0 x1 h4 y9 ff2 fs1 fc1 sc0 ls0 ws0">  <span class="ff1">其中 </span>,f( k)<span class="ff1">为有用信号</span>,s(k)<span class="ff1">为含噪声信号</span>,e(k)<span class="ff1">为噪声</span>,ε<span class="_ _0"> </span><span class="ff1">为噪声系数的标准偏差。</span></div><div class="t m0 x1 h4 ya ff2 fs1 fc1 sc0 ls0 ws0">  <span class="ff1">假设，</span>e(k)<span class="ff1">为高斯白噪声</span>,<span class="ff1">通常情况下有用信号表现为低频部分或是一些比较平稳的信号</span>,<span class="ff1">而噪声信号则表现为高频</span></div><div class="t m0 x1 h4 yb ff1 fs1 fc1 sc0 ls0 ws0">的信号<span class="ff2">,</span>我们对 <span class="ff2">s(k)</span>信号进行小波分解的时候<span class="ff2">,</span>则噪声部分通常包含在<span class="_ _0"> </span><span class="ff2">HL</span>、<span class="ff2">LH</span>、<span class="ff2">HH<span class="_ _1"> </span></span>中<span class="ff2">,</span>如下图所示，只要对</div><div class="t m0 x1 h4 yc ff2 fs1 fc1 sc0 ls0 ws0">HL<span class="ff1">、</span>LH<span class="ff1">、</span>HH<span class="_ _1"> </span><span class="ff1">作相应的小波系数处理</span>,<span class="ff1">然后对信号进行重构即可以达到消噪的目的。</span></div><div class="t m0 x1 h5 yd ff2 fs2 fc1 sc0 ls0 ws0"> </div><div class="t m0 x1 h7 ye ff1 fs3 fc1 sc0 ls0 ws0">正弦信号采用<span class="_ _2"> </span><span class="ff2">db1<span class="_ _2"> </span></span>进行去噪</div><div class="t m0 x1 h6 yf ff2 fs1 fc0 sc0 ls0 ws0">t = -10:.1:10;</div><div class="t m0 x1 h4 y10 ff2 fs1 fc0 sc0 ls0 ws0">% <span class="ff1">干净的信号</span></div><div class="t m0 x1 h6 y11 ff2 fs1 fc0 sc0 ls0 ws0">ori_sig = sin(t);</div><div class="t m0 x1 h4 y12 ff2 fs1 fc0 sc0 ls0 ws0">% <span class="ff1">加上噪声之后的信号</span></div><div class="t m0 x1 h6 y13 ff2 fs1 fc0 sc0 ls0 ws0">signal = ori_sig + 0.2 * randn( size(t) );</div><div class="t m0 x1 h4 y14 ff2 fs1 fc0 sc0 ls0 ws0">% <span class="ff1">信号长度</span></div><div class="t m0 x1 h4 y15 ff2 fs1 fc0 sc0 ls0 ws0">% 1<span class="_ _1"> </span><span class="ff1">层小波分解</span></div><div class="t m0 x1 h6 y16 ff2 fs1 fc0 sc0 ls0 ws0">sigLen = length( signal );</div><div class="t m0 x1 h6 y17 ff2 fs1 fc0 sc0 ls0 ws0">[cA1, cD1] = dwt( signal, 'db1' );</div><div class="t m0 x1 h4 y18 ff2 fs1 fc0 sc0 ls0 ws0">% <span class="ff1">系数构建</span></div><div class="t m0 x1 h4 y19 ff2 fs1 fc0 sc0 ls0 ws0">% A1 <span class="ff1">是信号的近似系数</span></div><div class="t m0 x1 h4 y1a ff2 fs1 fc0 sc0 ls0 ws0">% D1 <span class="ff1">是信号的细节系数</span></div><div class="t m0 x1 h4 y1b ff2 fs1 fc0 sc0 ls0 ws0">% <span class="ff1">在这里 </span>A1<span class="_ _1"> </span><span class="ff1">就可以近似地被视为信号去噪后结果，而<span class="_ _1"> </span></span>D1<span class="_ _1"> </span><span class="ff1">可以被视为噪声信号</span></div><div class="t m0 x1 h6 y1c ff2 fs1 fc0 sc0 ls0 ws0">A1 = idwt( cA1, [], 'db1', sigLen );</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div> </body> </html>